The present invention relates to amorphous patterns useful in manufacturing three-dimensional sheet materials that resist nesting of superimposed layers into one another. The present invention further relates to a method of creating such patterns which permits the patterns to be seamed edge-to-edge with themselves or other identical patterns without interruptions in the form of visible seams in the pattern.
The use of amorphous patterns for the prevention of nesting in wound rolls of three dimensional sheet products has been disclosed in commonly-assigned, co-pending (allowed) U.S. patent application Ser. No. 08/745,339, filed Nov. 8, 1996 in the names of McGuire, Tweddell, and Hamilton, entitled xe2x80x9cThree-Dimensional, Nesting-Resistant Sheet Materials and Method and Apparatus for Making Samexe2x80x9d, the disclosure of which is hereby incorporated herein by reference. In this application, a method of generating amorphous patterns with remarkably uniform properties based on a constrained Voronoi tesselation of 2-space was outlined. Using this method, amorphous patterns consisting of an interlocking networks of irregular polygons are created using a computer.
The patterns created using the method described in the above mentioned application work quite well for flat, small materials. However, when one tries to use these patterns in the creation of production tooling (such as embossing rolls), there is an obvious seam where the pattern xe2x80x9cmeetsxe2x80x9d as it is wrapped around the roll due to the diverse edges of the pattern. Further, for very large rolls, the computing time required to generate the pattern to cover these rolls becomes overwhelming. What is needed then, is a method of creating these amorphous patterns that allows xe2x80x9ctiling.xe2x80x9d As utilized herein, the terms xe2x80x9ctilexe2x80x9d, xe2x80x9ctilingxe2x80x9d, and xe2x80x9ctiledxe2x80x9d refer to a pattern or pattern element comprising a bounded region filled with a pattern design which can be joined edge-wise to other identical patterns or pattern elements having complementary but non-identical edge geometries to form a larger pattern having no visually-apparent seam. If such a xe2x80x9ctiledxe2x80x9d pattern were used in the creation of an embossing roll, there would be no appearance of a seam where flat the pattern xe2x80x9cmeetsxe2x80x9d as it is wrapped around the roll. Further, a very large pattern (such as the surface of a large embossing roll) could be made by xe2x80x9ctilingxe2x80x9d a small pattern, and there would be no appearance of a seam at the edges of the small pattern tiles.
Accordingly, it would be desirable to provide a method of creating amorphous patterns based on a constrained Voronoi tesselation of 2-space that can be xe2x80x9ctiledxe2x80x9d with no appearance of a seam at the tile edges.
The present invention provides a method for creating amorphous patterns based on a constrained Voronoi tesselation of 2-space that can be tiled. There are three basic steps required to generate a constrained Voronoi tesselation of 2-space: 1) nucleation point placement; 2) Delauney triangulation of the nucleation points; and 3) polygon extraction from the Delauney triangulated space. The tiling feature is accomplished by modifying only the nucleation point portion of the algorithm.
The method of the present invention, for creating an amorphous two-dimensional pattern of interlocking two-dimensional geometrical shapes having at least two opposing edges which can be tiled together, comprises the steps of: (a) specifying the width xmax of the pattern measured in direction x between the opposing edges; (b) adding a computational border region of width B to the pattern along one of the edges located at the x distance xmax; (c) computationally generating (x,y) coordinates of a nucleation point having x coordinates between 0 and xmax; (d) selecting nucleation points having x coordinates between 0 and B and copying them into the computational border region by adding xmax to their x coordinate value; (e) comparing both the computationally generated nucleation point and the corresponding copied nucleation point in the computational border against all previously generated nucleation points; and (f) repeating steps (c) through (e) until the desired number of nucleation points has been generated.
To complete the pattern formation process, the additional steps of: (g) performing a Delaunay triangulation on the nucleation points; and (h) performing a Voronoi tessellation on the nucleation points to form two-dimensional geometrical shapes are included. Patterns having two pairs of opposing edges which may be tiled together may be generated by providing computational borders in two mutually orthogonal coordinate directions.